More than 125 migrant mothers and children have sued the U.S. government, claiming the Trump administration has violated the rights of asylum-seekers through the arbitrary and capricious implementation of a virtual asylum ban at the southern border.

The lawsuit, filed late on Monday, was the first to challenge President Donald Trump over asylum since the U.S. Supreme Court decided last week that an anti-asylum rule will be allowed to take effect while a separate lawsuit on its underlying legality is heard.

Unlike other suits that have targeted the asylum rule itself, the latest filing challenges the Trump administration on procedural grounds, saying the government has enacted changes without warning, resulting in elevated rejection rates for asylum-seekers.

With the administration rolling out a series of anti-immigration regulations in rapid succession, asylum-seekers are not being told which of the shifting standards will apply to their cases, said Hassan Ahmad, the lead attorney on the lawsuit.

"What we're challenging is the haphazard lack of legal procedure. There's no rhyme or reason to it," Ahmad said.

The plaintiffs are 126 women and children from 59 families, mostly from the impoverished and violent Central American countries of El Salvador, Honduras and Guatemala, who were rejected in the early stages of the asylum process while staying at the South Texas Family Residential Center in Dilley, Texas.

The suit was filed in U.S. District Court in Washington, D.C.

Trump's virtual asylum ban at the southern border denies migrants if they did not first seek safe haven in another country that they traveled through on the way to the United States, such as Mexico or Guatemala.